The splitting theorem for globally hyperbolic Lorentzian length spaces with non-negative timelike curvature

DOI10.1007/s11005-023-01668-wzbMath1522.53024arXiv2209.14724OpenAlexW4366261668WikidataQ121746793 ScholiaQ121746793MaRDI QIDQ6097988

Tobias Beran, Felix Rott, Argam Ohanyan, Didier A. Solis

Publication date: 7 June 2023

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.14724

zbMATH Keywords

splitting theoremsLorentzian length spacessynthetic curvature bounds

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items (2)

Gluing of Lorentzian length spaces and the causal ladder ⋮ On conformal Lorentzian length spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A splitting theorem for the weighted measure
• An overview of the proof of the splitting theorem in spaces with non-negative Ricci curvature
• A splitting theorem for Alexandrov spaces.
• Aspects of \(C^0\) causal theory
• A cone splitting theorem for Alexandrov spaces
• A proof of the splitting conjecture of S.-T. Yau
• Lorentz and semi-Riemannian spaces with Alexandrov curvature bounds
• Two generalizations of Cheeger-Gromoll splitting theorem via Bakry-Emery Ricci curvature
• Splitting theorems for spatially closed space-times
• Decomposition theorems for Lorentzian manifolds with nonpositive curvature
• The splitting theorem for space-times with strong energy condition
• Remarks on cosmological spacetimes and constant mean curvature surfaces
• The Lorentzian splitting theorem without the completeness assumption
• The splitting theorem for orbifolds
• A splitting theorem for manifolds of almost nonnegative Ricci curvature
• Inextendibility of spacetimes and Lorentzian length spaces
• Timelike completeness as an obstruction to \(C^{0}\)-extensions
• A generalization of the Cheeger-Gromoll splitting theorem
• Lorentzian length spaces
• Causal completions as Lorentzian pre-length spaces
• Existence of CMC Cauchy surfaces and spacetime splitting
• On the geometry of metric measure spaces. I
• The splitting theorem for manifolds of nonnegative Ricci curvature
• On the structure of complete manifolds of nonnegative curvature
• On Lorentzian causality with continuous metrics
• Ends of Riemannian manifolds with nonnegative Ricci curvature outside a compact set
• A Splitting Theorem for Complete Manifolds with Nonnegative Curvature Operator
• Seminar on Differential Geometry. (AM-102)
• A new topology for curved space–time which incorporates the causal, differential, and conformal structures
• A.D. Alexandrov spaces with curvature bounded below
• Local Splitting Theorems for Riemannian Manifolds
• Regularity of Lorentzian Busemann Functions
• On the causal hierarchy of Lorentzian length spaces
• Causality theory of spacetimes with continuous Lorentzian metrics revisited
• Causality theory for closed cone structures with applications
• Riemannian spaces which contain straight lines
• The metric structure of Riemannian spaces with nonnegative curvature which contain straight lines
• Optimal Transport
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

This page was built for publication: The splitting theorem for globally hyperbolic Lorentzian length spaces with non-negative timelike curvature